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By N. Johnson, J. Quinteros

With the general trend across all commodities towards the treatment of lower grade ores, it is becoming increasingly important to develop efficient protocols for comprehensive mineralogical characterisation to allow the development of the most appropriate strategies for processing an ore. In the case of silver, there are more than 200 known silver bearing minerals which can make it challenging to identify them. Knowledge of the deportment of silver within an ore is one of the factors used to determine an appropriate processing strategy. Automated SEM-based tools are commonly used for mineralogical characterisation but the low-grade together with the large number of minerals that are potential hosts for silver means that often, complementary analytical tools must be used in order to properly account for the silver. The work presented in this paper is a demonstration of the approach that should be taken when identifying the deportment of silver in complex ores. Three complex, low-grade silver ores were characterised using the approach. The insights from the mineralogical characterisation were then used to inform the metallurgical testing that was undertaken. The results from the batch flotation testing clearly demonstrate the importance of understanding the mineralogy in order to select the most appropriate metallurgical processes.

Jan 1, 2014

High flotation of iron sulfide minerals at high pH values in copper ores is mainly due to the activation of these minerals by copper species dissolved from copper sulfide minerals during grinding. Several methods have been tested to reduce this copper activation during grinding and therefore to depress iron sulfide flotation. They include grinding the minerals at high pH values or with a less reactive medium such as high chrome, and addition of a thiol collector or copper complexant during grinding. The efficacy of these methods in the flotation of a copper ore was tested against more common methods of depression of iron sulfide flotation. The mechanism of iron sulfide depression in these methods was also investigated.

Jan 1, 2014

By L. Semushkina

Next generation flotation agents of KSK series for the concentration of complex copper-lead ores and the new ferromagnetic nanosized depressor of galena are introduced in this work. The feature of the KSK flotation agents is that they exhibit both frother and collector properties. KSK-6 can successfully substitute the widely used in Kazakhstani industry reagent ?-80 at the reduced consumption of butyl xanthate by 30 %. The new ferromagnetic nanosized depressor of galena, besides a low consumption rate of 100 g/t, also makes possible to exclude sodium sulfite (3-4 kg/t) and ferrous sulfate (5-6 kg/t) from the separation process, and receive high metal grade concentrates. Keywords: complex copper-lead ore, flotation agent, concentration method, ferromagnetic nanosized depressor

Sep 1, 2012

By A. V. Myaskov, V. S. Valavin, K. D’Elia, I. O. Krylov, Vu Van Toan, T. I. Yushina

"The purpose of this research is the development of a technology for processing the concentration tailings of limonite ores at Kamysh-Burun Mining and Processing Complex into an iron- containing product for ROMELT process. In the concentration and metallurgical processing of iron ores, substantial amounts of waste are generated (tailings, slimes, slags, metallurgical dust, etc.) that can be converted into a commercial product if is properly processed. This article presents the results of experimental studies of the feasibility of processing iron- containing tailings of Kamysh-Burun deposit (slimes from Verkhne-Churbash storage facility (VCh sample) and dumped waste of Kamysh-Burun (KB sample)) to obtaining valuable components for further uses. Applying Mossbauer spectroscopy has been shown that the iron minerals in the studied samples are technogenic varieties of iron hydroxides. The most suitable technology is the magnetic roasting process, since iron hydroxides are easily transformed into a magnetic, easily recoverable form. Have been shown the advantages of a two-stage magnetic separation, in a strong field and with polygradient separators. Concentrating this material through magnetic methods makes it possible to increase the iron content to 20-21 %. Magnetic concentration of the deeper layers materials results in iron- containing concentrates with a total iron content of up to 58% whit a phosphorus content of about 2%. Reducing the phosphorus content is possible by blending upper and lower layers of the material at a ratio of 1:1. Thus, it is possible to process the material accumulated in the slime storage facility using the ROMELT process combined with preliminary three-stage magnetic concentration and disposal of tailings with the permissible iron content of less than 5%. Wastes from smelting will be slags suitable for use in construction industry. The Kamysh-Burun material preparation for ROMELT process should be performed applying gravity-washing with separation of the -0.4 mm fraction and additional blending for dephosphorizing the concentrate. The smelting will produce pig iron and slag."

Jan 1, 2018

By J. K. Qu

As one of the key inorganic chemical industries, the chromate chemical industry has spawned extensively public concerns due to the resulted environmental pollution. The cleaner production technology for chromium compounds bases on sub-molten salt medium developed by the Institute of Process Engineering, Chinese Academy of Sciences has greatly decreased the reaction temperature and energy consumption, significantly in-creased the utilization ratio of the chromium element, and successfully achieved the comprehensive utilization of chromite resources and zero emission of chromium-containing residue. The separation process of production is the most important components in the cleaner technology. In this work, we studied two parts: the first is the removal of SiO2, Al3+ from the system and the recycling utilization of alkali metal medium through adding Ca(OH)2 and CaO; the second is to get more pure K2CrO4 crystalloid and remove K2CO3 from KOH solution through evaporation to prepare raw material for manufacturing Cr2O3 and get 50%(wt) KOH. The results obtained show that Ca(OH)2 can remove Al3+ more than CaO and has lower caustic ratio than CaO when they were added 110% of theoretic quantity. The optimal pure K2CrO4(96%) can be gained at 45 Celsius degree in 30% KOH solution and K2CO3 in 50% KOH solution could be decreased to 3.5%(wt) at 40 Celsius degree. And then K2CO3 can be causticized with adding Ca(OH)2 to recycle potassium alkali. The impure material can be re-moved and suitable raw material for manufacturing Cr2O3 can be gotten and reaction medium can be also recycled in this process technology, realizing cleaner production effectively.

Jan 1, 2014

By J. D. Miller, C. L. Lin

In general, x-ray computed tomographic (CT) techniques are able to provide 3D images of the internal structure of opaque materials in a nondestructive manner. The unique cone beam geometry allows acquisition of all 2D projections with only one rotation of the sample thus providing for fast data acquisition and better x-ray utilization, as a complete 2-D detector array receives the cone-shaped flux of rays. Thus, an isotropic 3D volume can be reconstructed without the mechanical translation and the stacking of sequential slices as is the case for more conventional CT scanners. In this regard, a state-of-theart, custom designed x-ray microtomography facility to provide very detailed 3D spatial analysis of multiphase particles has been installed and is in operation at the University of Utah. The reconstructed 3D tomographic volume allows for an adjustable spatial resolution from 5 to 20 microns for sample dimensions from 10 to 40 mm in diameter, respectively. For example, a packed bed of coal particles is shown below in which different crystalline froms of pyrite are distinguished in 3D.

Jan 1, 2003

By G. R. Forbes

Flotation froth machine vision systems provide consistent real-time measurements pertaining to the state of the flotation cell being monitored. Typical measurements include froth velocity, froth colour, froth texture and froth stability. This paper presents the results from test work conducted on the molybdenite rougher circuit at the Kennecott Utah Copper Concentrator during February 2006. Machine vision results show that it is not possible to accurately determine bubble size distribution information for the molybdenite froth, despite using state-of-the-art methods. Instead, it is necessary to make use of texture measurements to classify the various different froth states. Numerous combinations of texture measurements and classifiers are used to determine the best combination. Results show that the Fourier ring based texture measurements perform the best when both K nearest neighbour and Gaussian mixture model classifiers are used. The concentrate grade of the flotation cell is modelled using combinations of froth velocity and froth texture descriptors. The results show that by using a linear combination of these descriptors rather than either one by itself it is possible to account for a much larger percentage of the variation observed in the concentrate grade data. Adjusted R2 values of 92% and 84% are achieved when modelling the copper and the molybdenite concentrate grade respectively.

Jan 1, 2014

By M. I. Panayotova

Some of effluents released by copper smelting plants are highly acidic (pH = 0~1) and contain arsenic and copper in relatively high concentrations (10~20 g/L). Usually arsenic is removed by precipitation with different reagents, such as lime, iron salts, calcium salts, aluminium salts, etc. Precipitates (often voluminous) that require further handling are formed and copper and other valuable components are lost. A method is presented for copper and arsenic extraction from acidic effluents. Effluents are treated in specially designed closed electrochemical cell without chemicals? addition. Gases formed are collected and treated for decomposing the eventual traces of As-bearing compounds and ensuring the environment protection. Initially copper of grade of 85 % is electro-won. Further about half of the initially available arsenic is separated as low-soluble, low volume mixture of intermetallic compounds, oxides and some elemental arsenic. At the next stage the main part of the left arsenic is immobilized as low soluble stable compound. Arsenic content in the treated acid is in the range 0.20~0.25 g/L. Acidity of treated effluent after first two stages remains practically unchanged and the solution can be re-used. Physicochemical and electrochemical processes, governing copper and arsenic removal, are discussed.

Jan 1, 2014

By Rogerio de Oliveira Baldoino

The sedimentary phosphate deposit of Bayovar is located in a very dry area of Peru (desert of Sechura) which is close to the Pacific coast. It consists of seven superposed layers (beds) which call for different strategy of concentration. The ore is composed predominantly by apatite (84% in weight basis) plus silicates (16%). In order to treat the ore from beds 1-5, a suitable standard mineral processing circuit (composed of scrubbing, screening, attrition and desliming) started its operation in 2010, yielding 3.9 Mt/y of concentrate assaying 30% of P2O5. To concentrate phosphate from beds 6-7, however, it is necessary to carry out further cationic reverse flotation of silicates, at neutral pH, to yield a concentrate, which meets market specification. The new process was developed in laboratory scale by a collaborative program conducted between Vale S.A. and the University of Sao Paulo-Brazil. A pilot plant has currently been running in order to confirm the very good results yielded in laboratory scale. The successful accomplishment of flotation in the current beneficiation flow sheet will enable a capacity expansion of 1.9 Mt/y of concentrate assaying 30% of P2O5. As water resources are very limited at Bayovar region, all the steps of concentration, including flotation, must be performed with seawater, which must be continuously recycled. This work addresses some relevant topics related to the use of seawater in the reverse cationic flotation of silicates: influence of temperature, water quality (ageing and chemical composition) and collector type (ether amine versus condensate). The results indicate that condensate amine works better than ether amine. If flotation is conducted with the former collector, the separation process is able to tolerate changes in temperature (25-40oC) and water quality caused by either evaporation or ageing. Keywords: phosphate, flotation, seawater, temperature, ageing, concentration, salt

Sep 1, 2012

By A. J. Lynch, L. Ergun, M. Oner

"A research program on modelling cement grinding circuits has been in operation at Hacettepe University, Ankara, for four years. It has concentrated so far on tube mill and air separator grinding circuits for cement clinker, with emphasis on plant sampling surveys, including axial sampling inside the tube mills. The methodology is to use plant data to build the models and to supplement this by laboratory data where necessary, for example the determination of breakage functions. The plant data come from comprehensive sampling surveys and so far 33 surveys of clinker grinding circuits have been carried out in 9 plants. The operating conditions have been• mill sizes – 3.2 to 4.8 metres diameter and 8.5 to 15 metres long,• mill feed rates – 46 to 158 tonnes per hour,• air flow through mills – 25000 to 125000 cubic metres per hour,• cement clinker work indexes – 10.3 to 18,• separator sizes – 2. to 3.1 metres diameter,• separator feed rates – 132 to 689 tonnes per hour,• separator speeds – 12.3 to 21 metres per second.The ball mill model is Whiten’s perfect mixing model and the separator model is the Tromp curve with a fish-hook. This paper emphasises on the importance of calculating the breakage rates and the discharge functions with three case studies at five different circuits which were selected for discussion because they show how particular features of circuit operation can be included in the general models. Size distributiongraphs are used to illustrate every aspect of the discussion.In case I the special emphasis on calculating the breakage rates and discharge rates separately is given in a high pressure grinding roll-ball mill-separator circuit. The tonnes of each size fraction in the mill and the calculated values of R/D, D and R are determined. The values of R per mw are also given to allow comparison with mills of other sizes. The circuit allows the comparison of the static type (V Sep) and dynamic type separators (SKS). Comparing the reduced efficiencies shows that the dynamic separator is slightly more efficient than the static one.In case 2 data are given from two compartment tube mills having the same diameter and the motor power but different ball size gradation. The breakage rate particle size variation of the second chamber of two mills indicate that having finer ball size distribution causes higher breakage rate values."

Jan 1, 2003

By M. Gonzalez Fernandez

"Commercially introduced in 2004, the SAGDesign™ test has today proved its efficiency for sizing SAG mills for a wide variety of ores, from very soft to very hard ones. The interest of building a model using the SAGDesign™ test specific energy is the introduction of such a model into a complete process simulator making it possible to predict a complete material balance. The developed model compares the required specific energy with the energy provided by the mill. This energy calculation is derived from the Austin Power Formula. The specific energy provided by the test is corrected, using various parameters, such as the Ball Mill Work Index, to take into account the true operating conditions, the feed and product sizes. The core of this model allows the determination of the product d80 using the mill geometry, its operating conditions and of course the SAGDesign™ test results. To be included in a simulator, the model must also predict the overall size distribution of the SAG mill discharge. Assumptions to answer this point are presented here. The model has been implemented in the USIM PAC simulator. It is used either to predict the product size distribution for a given SAG mill, but also to size a SAG mill for getting a required reduction ratio. INTRODUCTION Over the last few years several types of new comminution machines have been introduced in the market. The most notable newcomer was the HPGR (Morley, 2006). But, even when these machines have some advantages, they have not earned the trust of the mining industry. That is why the established technologies still being the first choice. And, in comminution, that first choice are SAG and ball mills. The design of ball mills has been well understood for a long time. The Bond Ball Mill Work Index is the standard test which helps to describe the ore in terms of energy requirements for milling. Unfortunately, the development of an equivalent test to characterize the ore subject to SAG milling has taken some time. As of today, several tests are available in the market, like the MacPherson test, the MinnovEX SAG Power Index (SPI™), the JK Drop Weight Test, the SMC Test® and the SAGDesign™ test (Verret et al., 2011). The SAGDesign™ test, developed by John Starkey in Canada in the early 2000s (Starkey et al., 2008, 2015), has become one of the standards to assess the grindability of an ore in a SAG mill. One of its advantages is the reduced sample mass needed to perform it, hence, the reduced cost. The second one is that the output of the test is straightforward, it is the energy required to grind the ore between two sizes. Because of this energetic approach, the results provided by the test can be directly applied to size a new mill or to assess the performance of an existing mill."

Jan 1, 2018

By Peter N. Holtham, Geoffrey J. Lyman, The University of Queensland, Matthew S. Brennan, Vijay Subramanian, Rui X. Rong

"The cyclone would have a claim to be the commonest, least understood and most abused piece of mineral processing equipment available for study by researchers. It has certainly generated its fair share of publications – 1,000 in the last 60 years would be a fair estimate. However this remarkable degree of interest and scale of investigation is not reflected in our understanding of how they work; cyclones are still installed inappropriately and run poorly, which suggests that there are still things to learn about this deceptively simple process.In mineral processing there are two broad classes of cyclone: the hydrocyclone, used in classification, thickening and dewatering, and the dense medium cyclone, used for concentration by density. Although rarely studied together, the laws of physics presumably apply equally to both and so it seems that there would be interesting things to learn by considering them as a single class of device. The good news is that in recent years there have been spectacular advances in the computational and measurement tools available to study these devices, including computational fluid dynamics (CFD), tomography, and laser doppler anemometry (LDA), and some good progress has been made in an understanding of the fundamental principles involved.The JKMRC has made many experimental studies of hydrocyclones and DM cyclones, leading to useful empirical models. However some recent CFD and tomographic work, in association with work of other institutions, has thrown important light on the workings of these processes. Progress has also been made in novel designs of cyclone to achieve improved separating efficiency, based on an attack on the subprocesses believed to contribute to inefficient operation. This paper describes the work to date.Modelling of the dense medium and classifying cyclone was conducted using the Fluent computational fluid dynamics code. Three phase simulations of the dense medium application (air/water/medium) showed appropriate medium segregation effects but over-predicted the level of segregation compared to segregation measured by gamma-ray tomography. This is believed to be because the basic Algebraic Slip mixture model in Fluent does not model any back-mixing of the dispersed phase due to turbulence."

Jan 1, 2003

By B. Das

The separation of iron values from a typical Indian iron ore slimes containing 57.2% Fe, 5.81% SiO2 and 7.05% Al2O3 by wet magnetic separation and selective magnetic coating is investigated. The iron phases, which are mostly paramagnetic in nature, have been coated with magnetite or colloidal magnetite in presence of surfactant by manipulating the surface properties of the minerals. The studies have indicated that an iron concentrate containing 62.32% Fe with 66.5% iron recovery can be obtained at medium magnetic intensity of 7.8 kG which is much less compared to normal magnetic intensity of 13 kG to14 kG required for hematite-goethite separation. The performance of this technique with respect to both grade and recovery is superior to conventional magnetic separation or flotation of iron ore slimes.

Jan 1, 2014

By Genrich A. Denisov

Principles of ecologically friendly geo-technologies construction are formulated on the basis of the works of the leading scientists in the field of rational processing of mineral resources of the Russian Academy of Sciences. One of these concepts is a new direction in rotational disintegration of mineral and technogenic raw material with the purpose of effective subsequent enrichment. A large amount of practical experience has been accumulated in the industry on selective destruction by application of vibrational method on initial material with consideration of its physical-mechanical properties and mineral structure. This method is successfully realised in a conic inertial pulverisation devices constructed by Mekhanobr Institute (St.-Petersburg). A new construction of conical-inertial pulverisation with a modification of disintegration force has been developed recently at Mekhanobr Institute. It allows, in some cases, to increase selectivity of subdivision and to avoid over-disintegration. Advantages of “wet” subdivision methods in conic inertial disintegration devices are proved. The efficiency of such subdivision can be increased due to rational use of the phenomenon of a dislocation-dynamic diffusion. Its advantage is proved by the effect on disintegrated material by frequency-modulated variable electrical fields of low power. It was shown in industrial conditions, that the productivity of the spherical mill can be increased by 10 %, and that it also prevents ecologically harmful surface active substances (SAS) in milling zone and it reduces the dust content in the air. The techniques of tentative estimation of efficiency of various proceedings technogenic materials and their classification are created. The scientific fundaments of rational, ecologically friendly technology of processing and regeneration of various kinds of technogenic raw material are developed. A number of effective technologies on processing of wastes is developed and inculcated in concentration factories and metallurgical factories.

Jan 1, 2003

By N. Acarkan

Slags usually contain some quantity of valuable metals. They are actually a secondary resource of metals, rather than an end-waste and have been utilized as a resource material in many areas. In addition, for some applications, slags have comparable or even better properties than their competitors. Leaching is a method for extraction of metals from copper slags. The extraction of metals such as copper and cobalt from the copper slag of Küre-Turkey, was investigated in the past decades. Fayalitic type of these copper slags containing 0.934 % Cu, 0.353 % Co and 50.91% Fe were subjected to the experimental study. As a result of mineralogical analysis of the slag sample, fayalitic type of slag was found to contain hercynite, magnetite, hematite, pyrite, chalcopyrite, covellite, bornite and metallic copper. Direct acid leaching methods were applied on the sample. Effects of leaching time, temperature and acid concentration on Cu and Co leaching recoveries were investigated in the direct acid leaching. The optimum leaching conditions were found as leaching time of 2 hours, solid/liquid ratio of 1/3, H2SO4 concentration of 125 g/L and temperature of 70 °C. At these conditions, 75.5 % of Cu, 95.6 % of Co and 70.9 % Fe were extracted. In the second stage of the leaching experiments, copper in the pregnant solution was precipitated by cementation to produce a Cu concentrate assaying 95.58 % Cu; cobalt was obtained by precipitation with H2S to produce a concentrate containing 62.10 % Co. As a result of this study a process flow sheet has been developed for recovering Cu and Co from these slags to demonstrate its economic and technological benefits.

Jan 1, 2014

By Fu Ping-Hao, Sergio Mauricio Vianna, Ewen Silvester, Emmy V. Manlapig

"Over the last 5 years, an ambitious project has been undertaken at the Julius Kruttschnitt Mineral Research Centre (JKMRC) aiming to isolate, study and, if possible, model the effect of particle size, liberation and collector adsorption density on the floatability of mineral particles. As part of this project, we have conducted highly controlled flotation test-work, combined with state-of-the-art solution and surface analytical techniques such as High Performance Liquid Chromatography (HPLC), Time of Flight Secondary Ion Mass Spectroscopy (TOF-SIMS) and detailed mineralogical analysis to fully characterize the flotation behavior of a natural ore.The flotation tests were undertaken using a high-grade lead-zinc ore from BHP-Billiton’s Cannington mine (Australia) in a specially designed continuously operated laboratory scale flotation rig. Solution and adsorbed collector concentrations were measured independently during the course of the flotation tests using HPLC based ex-situ techniques. Liberation studies were performed using the JKMRC Mineral Liberation Analyser (MLA) on selected size intervals of different streams to estimate the specific surface area of galena. These results were used to calculate the collector adsorption density (collector coverage) on galena particles, with the eventual aim of developing a mathematical model describing the relationship between pulp chemistry, feed mineralogy, and floatability of galena particles."

Jan 1, 2003

By Y. F. Guo

Laboratory scale experiments were conducted to produce titanium-rich material from Panzhihua ilmenite. The results showed preoxidation with sodium salt additive especially for Na2B4O7 signif- icantly advance the reduction of iron in Panzhihua ilmenite. Acceleration mechanism of preoxidation with Na2B4O7 has been studied here. The maximum metallization of iron 92% can be obtained under conditions of preoxidation at 850? for 30 min and subsequent reduction at 1100? for 150 min. The rusting separation technique to reduced ilmenite has been further studied, obtaining titanium-rich product with TiO2 over 82% and the recovery of TiO2 above 97%.

Jan 1, 2014

By C. Han

The analytical results of Dagushan grinding workshop primary grinding operation product show that the size fraction of -0.079mm is 32.88%, the size fraction of -0.01mm is 9.97%, the rate of -0.01mm size fraction and -0.079mm size fraction is 30.32%. It means that there is too much -0.01mm size fraction in primary grinding operation product and fall out that there will not be a better result in following operations. Several tests have been carried out to control the size distributing of the primary grinding operation product according to confirm the appropriate conditions of grinding operation. Integrate with theoretic count, grinding property tests show that the appropriate rev ratio of ball mill should be between 85% and 90% so as to get better size distributing. Based on the results of grinding property tests, the shocking property tests simulated the momentum of different diameter steel balls in the ball mill have been carried out. It showed that if want to get better size distributing the appropriate diameter of steel ball should be 110mm. The tests result shows that regulate diameter of steel ball and rev ratio of ball mill could control the size distributing. Contrast to the technical parameters of ball mill in grinding operation now, there are some significant advices are given for practice and industrial tests.

Jan 1, 2014

By A. Buchanan, M. Mirnezami, A. L. Restrepo, J. A. Finch, M. S. Hashemi

Settling rate studies on slurries from Cu/Zn flotation plants occasionally revealed two aggregation maxima at pH 8-10 and 10-12. From measurements on sphalerite and silica suspensions the double maxima were replicated by Zn ions (pH 8-10) and Mg ions (pH 10-12) corresponding to the presence of zinc hydroxide and magnesium hydroxide, respectively. A combination of chemical and electrostatic bridging by the hydroxides is considered to be the aggregation mechanism.

Jan 1, 2003

By B. Orberger

The fine fraction (< 2 mm) of the high grade Mn-ore from the world class Moanda deposit, Francevillan basin, in Gabon, contains up to 30 wt. % of manganese and about 0.4 wt. % phosphorous. A pilot study at laboratory scale integrating mineralogy and geochemistry before and after ultrasonic treatment was conducted on the fine fraction (< 2 mm) of oxidized Mn ore in order to reduce the phosphorous content and enrich this fraction in manganese. The fine fraction was dried, crushed at 2 cm and sieved at 2 mm. The two fractions (< 2 mm and 2 mm ? 2 cm) were investigated by X-ray diffraction and scanning electron microprobe ? electron dispersive spectroscopy analyses. Both fractions contain lithiophorite, cryptomelane and pyrolusite as Mn carrier, and goethite, muscovite, illite and quartz as contaminants. The Mn hydroxide nsutite was only found in the fraction 2mm ? 2 cm.The < 2 mm fraction is significantly richer in goethite, muscovite/illite, and quartz. Phosphorous carriers are mainly goethite (up to 2.8 wt. % P2O5), while the Mn minerals contain up to 0.8 wt. % P2O5. The Mn minerals are partly included in an agglomerate of goethite, muscovite/illite, and quartz. The < 2 mm fraction was treated by ultrasound for 30 s in normal water. Mineralogical and chemical analyses after ultrasound treatment showed that the Mn-minerals were largely liberated from the goethite-muscovite-illite agglomerate. Mass balance calculations show that after ultrasonic treatment the < 2 mm fraction was ? 50 % enriched in Mn and ?50 % impoverished in P.

Sep 1, 2012